Given that 18,24,and k + 14 are three consecutive terms of an arithmetic progression Find a) the common difference b) the value of k c)the first term if the 4^(th) term is 12. d) the sum of the first twelve terms of the progression.


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Question Number 35594 by Rio Mike last updated on 20/May/18

$G i v e n t h a t 18, 24, a n d k + 14 a r e$ $t h r e e c o n s e c u t i v e t e r m s o f a n$ $a r i t h m e t i c p r o g r e s s i o n F i n d$ $a) t h e c o m m o n d i f f e r e n c e$ $b) t h e v a l u e o f k$ $c) t h e f i r s t t e r m i f t h e 4^{t h} t e r m i s$ $12 .$ $d) t h e s u m o f t h e f i r s t t w e l v e t e r m s o f$ $t h e p r o g r e s s i o n .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 20/May/18

	$a) c . d = 6$ $b) k + 14 = 30$ $k = 16$ $c) a + (4 - 1) \times 6 = 12$ $a = - 6$ $d) s = \frac{12}{2} {2 \times - 6 + (12 - 1) \times 6}$ $= 6 (- 12 + 66)$ $= 6 \times 54$ $= 324$
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